Bruce has pledged silence on my definition of analyticity
and has maintained his pledge by declining to clarify
the notion "criterion for analytic truth" which features
prominently in his critique.
I intend nonetheless to take his critique seriously
and to make the most of it.
I do not find in it sufficient grounds to change my
mind about the definition of analyticity which I
will use in my proposed monograph. However I intend
to ensure that his criticisms, insofar as I understand
them, are fully addressed either in the monograph or
in the supporting collateral on my web site, and are
also responded to on hist-analytic.
This I will do in installments, of which this is the
first, and addresses only Aune's first paragraph.
On Monday 23 March 2009 20:32:52 Bruce Aune wrote:
>1. I continue to believe that Roger’s use of the expression
>“analytic” is idiosyncratic and misleading, but I think he is
>entitled to use it as he wants to, so long as he makes his meaning
>clear to others. They may, or they may not (as I believe), find his
>usage useful.
I'm not entirely sure of the meaning or significance of
describing my definition as idiosyncratic or misleading,
and since Bruce is not going to explain this to me I will
have to make my best guess at this.
"Idiosyncratic" is not by itself, in my mind, a significant
criticism. The closest critique I should be concerned about
would be that the concept defined is too far removed from
previous usage of the term "analytic" to have any bearing
on the philosophical debates which have centred around it.
I do believe that the concept I have defined is fully in
line with its most important predecessors (and had already
presented some arguments to that before Aune's last
contribution).
I now have arguments to the effect that the two most
common definitions of analyticity, viz: that of Kant
and that given by Ayer (inter alia), criticised by
Quine, and used as a starting point by Kripke and
equivalent to my definition in terms of necessity.
These informal arguments are backed up by formal models
and formal machine checked proofs.
To the best of my knowledge my usage is identical in
substance to that of Rudolf Carnap, though the presentation
differs in detail.
Carnap and I concur in considering analyticity and necessity
interdefinable, though Carnap defined necessity in terms of
analyticity where I define analyticity in terms of necessity.
Though many philosophers believe that Kant's
definition of analyticity in terms of subject
predicate judgements is narrower than the more
recent "true in virtue of meaning", I don't believe
this myself.
The usual reason for thinking Kant's definition
narrow is that it applies only to judgements in
subject-predicate form. However, assuming that
analyticity is preserved by logical equivalence,
it is easy to see that every judgement is
equivalent to one in subject predicate form:
Consider the judgement;
S
Define the two predicates P and Q as follows:
P x <=def=> x = x
Q x <=def=> P x /\ S
Then it is easy to see that:
S <=> All Ps are Qs
Suggesting that Kant's notion of analyticity is not
confined to statemnts in subject predicate form and
is equivalent to analyticity as "true in virtue
of meaning" which is in turn (by a previous
argument of mine, and also by tweaking one
of Carnap's) equivalent to the definition I proposed.
I am surprised to see Aune suggest that my definition
is "misleading", and feel some sense of injustice
that he should do so without explicitly stating
in what way he thinks it might mislead.
In casting around to understand this allegation the
following is the closest I have come.
My proposed definition is quite "up front" in
effectively rejecting Kripkean metaphysics.
Readers might suppose that I imagine that this can be
done without a direct rebuttal of Kripke's arguments,
and I suppose supporters of Kripke, or of Kant, might
think this somewhat underhand.
Well as it happens, I do think that the common belief
that Kripke's arguments refute the contrary doctrines
of logical positivism can be refuted in this way, i.e.
without reference to his arguments. This is because
Carnap defines necessity in terms of analyticity and
the thesis that there are no synthetic necessary truths
is obviously true in that context. Kripke's arguments,
if sound, can only be so in relation to concepts materially
different to those of the logical positivists.
Nevertheless I do not intend to rest on this, and will
offer more detailed explanations of how Kripke's
arguments fail to refute the logical positivists,
It is an advantage of the definition of analyticity
which I have chosen that it makes conspicuous a necessary
constraint which Kripke fails to observe.
That is, that in judging and comparing the concepts of
analyticity and necessity in the same language, the same
semantics must be used in both cases (i.e. for both
analyticity and necessity).
The relevant aspect of semantics is the truth conditions.
Both necessity and analyticity are determined by the truth
conditions of the judgement in question. By defining
analyticity in terms of necessity I ensure that the truth
conditions which are used in determining necessity are
also used in determining analyticity.
By contrast, what Kripke does is to use the hypothesis of
rigid designation to establish that certain propositions
are necessary, and then ignore the impact of this hypothesis
on the truth conditions of the proposition when denying
that the judgement is analytic. In fact I don't know
how he does arrive at the denial, is this just his
"intuitive reasoning" or is there some more substantial
argument. Does he present an argument to the effect that
the meaning of a rigid designator is not the thing designated?
I will check this out more thoroughly in due
course, but meantime, whatever his method, it should be
rejected. The features of the truth conditions on which
necessity depends suffice to establish analyticity.
Kripke's claims about meaning suffice to deny analyticity,
then they are incompatible with the hypothesis of rigid
designation.
Roger Jones